I have a collection of nodes $N_i$ and minimum distances $d_{i,j}$ between them like this (not all $d_{i,j}$ shown for visual clarity).
The task is to find a 2D graph (the (x,y) positions of each node) such that the enclosing perimeter (border of red polygon) is as small as possible subject to the distances between the nodes being not smaller than $d_{i,j}$. Is there an algorithm to solve this problem??